Central bank’s planning harks back to its preparations for a similar referendum in 1975

LONDON—Ahead of a referendum on the U.K.’s future in Europe, Bank of England officials worried about a run on the pound were secretly forming plans to raise interest rates, stop Britons from moving their cash to Ireland and close London’s foreign-exchange market.

The year was 1975 and central-bank officials were preparing for the possibility that Britons would vote to leave the European Economic Community, a forerunner of today’s European Union. Four decades on, the country is poised for a similar referendum on Britain’s...